Large Group Bargaining in a Characteristic Function Game

Abstract

This paper presents the results of an n-person characteristic function game played by between seven and and twelve players, one of whom was a monopolist. A factorial design allowed for analysis of the effects of group size, the availability of information, and communication opportunities for a series of seven trials. The data were compared to the game theoretic concepts of the core and Shapley value, (Shapley, 1953, Roth, 1977a), and to the predictions of the Weighted Probability model (Komorita, 1974). The findings indicated that the monopolist held a great deal of power, especially when communication among the players was not allowed. His payoffs increased over trials and approached the core in all of the conditions except when communicaion was available in seven and eight-person groups. The overall results were very close to the Shapley value and the predictions of the Weighted Probability model. The results were compared to an earlier study on a similar three-person game; increasing the group size seemed to be the primary case of the increase in the monopolist's payoffs.